trigonometry · worked example

Solve tan(30°) = √3/3

Method: ângulo notável. Verified step-by-step solution with our free AI math solver.
Problem

tan(30°)\tan(30°)

Step-by-step solution

  1. Em um triângulo 3030-6060-9090, as razões dos lados são 1:3:21 : \sqrt{3} : 2.

  2. Oposto/adjacente para o ângulo de 30°30°: tan(30°)=13\tan(30°) = \frac{1}{\sqrt{3}}.

  3. Racionalize: 1333=33\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}.

Answer

tan(30°)=33\tan(30°) = \tfrac{\sqrt{3}}{3}

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